An imaging radar is a microwave sensor used to make two-dimensional images of surfaces or objects, where the resulting image is a map of the microwave reflectivity of the surface or object. In civilian or remote sensing applications, the surfaces are typically the surface of the earth, with known applications extending to celestial objects such as the moon or the planet Venus. In military applications, the sensed object is often an object of tactical or strategic significance.
Imaging radars are usually installed on moving platforms, such as aircraft or satellites. In such cases, the motion of the sensor platform provides one of the imaged dimensions, although known motion of the sensed surface or object can be accommodated in the processing. The second dimension is provided by the flight time of the microwave energy, which is proportional to the range between the sensor and the object or surface reflecting the radar energy (this second dimension cannot be coincident with the sensor/object motion dimension). In other SAR cases, it is possible for the sensor to be stationary, with the motion of the imaged object providing the motion dimension.
In simple imaging radars, the resolution in the motion dimension is given by the width of the radar beam in the motion direction. Such radars are referred to as RARs, for real aperture radars. However, the resolution of such imaging radars is often too coarse in the motion dimension to be useful in certain applications.
In June 1951, Dr. Carl Wiley of the Goodyear Aerospace Corporation introduced the concept of synthetic aperture radar or SAR, in which fine resolution in the motion dimension was obtained by processing the Doppler frequency of the reflected radar signal. In the side-looking case, the motion dimension is always perpendicular to the range or pulse time dimension, although these two dimensions do not always lie upon the surface being imaged. A good exposition of the principles of SAR are given in the book by Harger (1970).
Up until approximately 1975, an image was usually made from the received SAR data using a coherent optical system based on the principles of Fourier optics. In such optical SAR processors, lenses illuminated by coherent wavefronts (from laser sources) can perform mathematical operations such as two-dimensional Fourier transforms needed to focus the data into SAR images. (Raney, 1982)
In the 1970's, digital computer technology had advanced to the point where SAR images could be made using digital signal processing techniques. Although the initial digital SAR processors were slow in comparison to the optical processors, it was soon recognized that better control over the processing parameters and equations could be exercised in digital processors, and that better quality images could be produced A comparison of optical and digital processing technologies and capabilities was given by Ausherman in 1977, at the time when the advantages of digital processing were becoming apparent to knowledgeable engineers in the field. Engineers at MacDonald Dettwiler and CCRS were some of the more sophisticated proponents of digital SAR processing; for example, see the papers by Bennett and Cumming in 1979.
The principles of synthetic aperture radar, and its digital processing can be stated as follows. A moving platform, such as an aircraft or satellite, carries a radar system which emits encoded pulses of microwave radiation at periodic intervals called the pulse repetition interval or PRI. The inverse of the PRI is called the pulse repetition frequency or PRF. For each transmitted pulse, the radar system receives the echo from certain objects or surfaces within the illumination boundaries of the radar beam. The received signal is demodulated in a coherent fashion so that the phase of the demodulated signal is an accurate representation of the instantaneous range between the radar and the reflecting object at the time of the emitted pulse. This demodulated signal is digitized and recorded in computer memory or on magnetic tape or disk, and is subsequently passed to the digital signal processor to focus the received information into radar images.
The platform is assumed to be travelling at constant speed in a straight line, or along a predictable curved path. (For most SAR systems, the receiver uses the same SAR antenna as the transmitter. This is referred to as a monostatic SAR. In some cases, the receiver is on a separate platform, or on the ground. This latter form of SAR is referred to as bistatic SAR.) If this is not the case, a motion compensation system is used to change the time of the transmitted signal and the phase and time delay of the received signal, to emulate the signal that would be received from a stable platform.
The PRF is high compared to the speed of the platform and the width of the beam, such that a given radar reflector is illuminated by many pulses while the platform travels past the reflector. The distance travelled by the platform during this reflector illumination period is referred to as the synthetic aperture. This distance is much longer than the antenna length in the motion direction or the physical antenna aperture.
The received SAR signal is in the form of a one-dimensional hologram in the along-track direction, and contains radar induced coding and reflector induced delay in the range direction. In its raw or received form, the SAR data is completely unfocused, as information essential to signal focussing or image formation is contained in the phase rather than the amplitude of the received data. The SAR processor uses a geometry model to deduce the phase that is created by each reflector in the illuminated area, and uses this phase information to derive the structure and values of an electronic matched filter which will unscramble or compress the received data. The length of the matched filter is the length of the synthetic aperture, and when the data is compressed, it has the approximate resolution that would be obtained from a conventional RAR with a physical antenna the length of the synthetic aperture.
More specifically, the geometry model is used to determine the precise range between the radar antenna and the reflector at each radar pulse that the reflector is illuminated. This sequence of range values is expressed in a so-called range equation, from which most of the digital processing parameters are derived.
In its simplest form, the digital SAR processor uses interpolators and convolution operators to apply the matched filter to the received data, in order to focus the data into an image. This is a very numerically-intensive operation, with approximately 3000 million adds or multiplies needed per second to generate an image from a typical satellite SAR in real time.
There are two main aspects of SAR data which complicate the processing operations. The first is that the data received from a given reflector is not orthogonal to the range or azimuth axes or coordinates when stored in computer memory. The computer's memory can be thought of as a rectangular grid, with one side (the rows) parallel to the radar beam or range direction, and the other side (the columns) parallel to the platform's motion direction (called the azimuth direction). Stated in another fashion, when the echo from each radar pulse is received and stored in computer memory as a range line (a row of range cells), the range cell number corresponding to the start time of a given reflector varies with pulse number or azimuth time.
In SAR terminology, this variation of range cell number of each received echo is referred to as range cell migration. In the processing algorithm this migration must be corrected in one or more of the processing steps, an operation referred to as range cell migration correction, or RCMC. In most processing algorithms, this migration is corrected prior to the application of the azimuth matched filter, but it can be combined with the azimuth compression operation. Unless RCMC is done accurately, the resolution, phase and registration of the image will suffer.
The second complicating factor is that the parameters of the azimuth matched filter, as well as those of the range cell migration correction operation vary with range and possibly also with azimuth. This non-stationarity means that simple matched filtering techniques cannot be used. Unless special provision is made for these non-stationarities, an accurately focused image will not result.
If the SAR antenna is pointed in a direction perpendicular to the direction of motion of the platform (relative to the imaged surface), the SAR is said to be operating in a broadside or zero-squint mode. If the antenna is pointed forward or backward with respect to this broadside direction, the SAR is said to be operating in a squinted mode. The squint angle is the angle between the beam centerline and the broadside direction, measured in the plane containing the beam centerline and the platform relative motion vector. This broadside direction is the direction to the zero-Doppler line, which is the locus of points on the surface of the imaged terrain where the azimuth Doppler frequency of the received signal is zero.
The success of the SAR processing operation depends upon the efficiency of the operations, and on the image quality of the focused image. Depending upon the requirements of the user, one or the other of these processing attributes will be dominant. As computers get faster, the tendency has been to concentrate more on image quality, which has been a driving factor in the subject invention.
In the early days of SAR processing, the image quality requirements were relatively simple, with the focussing of the detected image, or the achieved resolution, being the primary concern. However, as SAR processing technology advanced and users became more demanding, the requirements of SAR image quality have become more sophisticated. Current image quality measures now include:
1. range resolution, PA2 2. azimuth resolution, PA2 3. peak side lobes, PA2 4. integrated side lobes, PA2 5. contrast ratio, PA2 6. absolute registration accuracy, PA2 7. relative registration accuracy, PA2 8. absolute radiometric accuracy, PA2 9. relative radiometric accuracy, and PA2 10. target phase.
Particular attention is drawn to the image quality attribute of target phase. Until very recently, most SAR processors produced detected images, in which the information of the target phase was removed. However, with recent applications of SAR such as polarimetry and interferometry being developed in which the phase information is specifically used, the phase fidelity of the processed image is becoming important.
In general, phase is the most difficult of the image quality parameters to measure, and is the parameter which is most sensitive to processing errors. In particular, when the squint of the SAR beam exceeds a few degrees, the processing becomes more complicated, and it is more difficult to produce an image with accurate phase. In the subject invention, a SAR processing algorithm is developed which preserves image phase more accurately in the presence of moderate or large squint angles than previous algorithms.
The most straight-forward way of compressing SAR data is to use a time-domain convolution to match filter the data in the range and azimuth directions. In the range direction, the range matched filter compresses the encoded radar pulse or chirp, while in the azimuth direction, the azimuth matched filter compresses the synthetic aperture described above. The range and azimuth compression operations are usually done separately, although they can be combined into a single two-dimensional convolution operation. If range cell migration correction (RCMC) is needed, it is applied with a range-direction interpolator in the time-domain processor.
While virtually all radars use encoded or expanded pulses today, the range compression operation is sometimes done with an analogue device before the data enters the digital SAR processor. In this manuscript, it is assumed that the SAR data is to be range compressed in the digital SAR processor, as is commonly done in satellite SAR systems.
The time-domain processor is the most simple processor, and can be very accurate, as long as the matched filters and interpolator coefficients are defined with sufficient precision. However, it is very inefficient in terms of computer operations when the pulse lengths or the synthetic apertures are long, or when RCMC is needed. The synthetic apertures are long when an aircraft SAR is operated at long ranges or with long wavelengths, and are very long for virtually all satellite SARs.
To overcome the disadvantages of inefficiency of the time-domain algorithm, frequency-domain SAR processing algorithms were developed in the late 1970's. The algorithm which has gained the widest use is the so-called Range/Doppler algorithm, in which azimuth compression, and particularly RCMC, is performed in the range-image, Doppler-frequency domain. This algorithm became popular because of its high efficiency, its relatively simple implementation and its ability to accommodate a very general form of range equation in its RCMC and azimuth compression operations.
The range/Doppler algorithm was first conceived by C. Wu and colleagues at the Jet Propulsion Lab in 1976 (Wu, 1976 and 1982). Fundamental improvements were made to the algorithm by MacDonald Dettwiler personnel in 1977-79, most notably the incorporation of an interpolator in RCMC to reduce the paired-echo artifact (Cumming & Bennett, 1979). This algorithm was steadily improved during the 1980's, and MacDonald Dettwiler delivered approximately 15 range/Doppler SAR processors to customers around the world during this period. Improvements continue to be made to this popular algorithm; e.g., Smith developed a frequency-domain expansion of the range equation which allows processing parameters to vary across azimuth blocks in a seamless fashion (Smith, 1991).
One disadvantage of the range/Doppler algorithm is that its efficiency drops when an attempt is made to achieve the highest accuracy by updating the azimuth processing parameters every range cell. Another disadvantage is that the interpolator used to implement RCMC is the hardest part of the algorithm to implement, and is one of the largest sources of error in the algorithm.
To overcome these disadvantages, a number of scientists have been exploring the wave equation approach to SAR processing, using analysis and processing principles originally developed in the field of seismic signal processing. The seismic algorithms were developed by many people in the 1960's and 1970's, with notable work done by Stolt who introduced a change of variables which allowed the processing parameters to vary continuously with range (Stolt 1978).
Professor Rocca and his colleagues in Milano, Italy were the first to recognize the applicability of the seismic techniques to SAR processing. They introduced a compromise allowed by the relative scales of the SAR wavelength and geometry which led to a version of the wave equation algorithm which, although an approximation, eliminated the interpolation operation (Cafforio et al., 1988, 1991). While a significant advance in concepts, Rocca's algorithm proved to be no more efficient or accurate than the range/Doppler algorithm (Scheuer & Wong, 1991). In fact, in many cases it was less accurate, because his algorithm assumes that RCMC does not vary with range
Another wave equation algorithm development was made by Raney and Vachon (1989). By reintroducing the interpolator, they obtained another form of the wave equation algorithm which could handle large amounts of squint.
There is a significant common feature to be found among all wave domain algorithms described in the literature: they all assume that the range signal has already been focused, or, equivalently, that the unfocused range signal has no importance to wave domain processing steps. The new invention takes a radically different approach in this regard, as will be discussed below.
The wave equation approach is distinguished by the fact that many of the SAR processing steps (especially RCMC) are done in the two-dimensional frequency domain. This is fundamental to the wave equation formulation, which handles the SAR processing exactly for a particular form of SAR geometry which we will refer to as rectilinear geometry. Rectilinear geometry refers to the case where the range equation is exactly given by a hyperbola, with the curvature of the hyperbola proportional to 1/R.sub.0, where R.sub.0 is the range between the radar antenna and the reflector at the closest point of approach.
Rectilinear geometry applies to the case where the sensor is travelling in a straight line and the reflector is stationary. This is the case for many airborne SARs, but is an approximation for satellite SARs. The approximation is good enough to provide adequate focussing of most satellite SAR data, but is not good enough to provide accurate registration and phase in the focused image.
To summarize the current level of technology, both the range/Doppler and wave equation algorithms can produce well focused images in most cases, but a few disadvantages persist. The advantages of the range/Doppler algorithm are:
The disadvantages of the range/Doppler algorithm are:
The advantages of the wave equation algorithms are:
The disadvantages of the wave equation algorithms are:
It is seen from this list that the two algorithms are largely complementary. In other words, where one algorithm has a shortcoming, the other algorithm excels, and vice versa. The concept of the new invention, to be described below, is to introduce some new algorithm steps which allow the best features of these two algorithms to be combined, and at the same time eliminate most of their disadvantages.